It is worthwhile to note that the linearly polarized WW gluon distribution cannot be transformed from coordinate space into momentum space directly, this is because the tensor structure \(\frac{1}{2}(\delta ^{ij}-2\frac{r^i_\perp r^j_\perp }{r^2_\perp })\)  is different from \(\delta ^{ij}\) . After performing this projection, the tensor structure will naturally generate a \(-\cos (2\theta )\)  factor, where \(\theta \)  is the relative angle between \(r_\perp \)  and \(k_\perp \) . Alternatively, \(xG(x_g, k_\perp )\)  and \(xH(x_g, k_\perp )\)  can be arrived at by projecting \(xW^{ij}\)  onto \(\frac{1}{2}\delta ^{ij}\)  and \(\frac{1}{2}(2\frac{k^i_\perp k^j_\perp }{k^2_\perp }-\delta ^{ij})\) , respectively, which has been done in Refs. [1]}, [2]}.
